Chapter 6.5, Problem 4P

Graph each linear inequality.

$-4x+5y<-3$

To determine

To graph: $-4x+5y<-3$

Explanation of Solution

Given information: $-4x+5y<-3$

Graph:

  Interpretation: The boundary of the graph is the graph of $-4x+5y=-3$ . Since, the inequality symbol is <, the boundary is dashed.

The point $(0,0)$ has to be checked as it is not on the boundary line.

  $\begin{array}{l}-4x+5y<-3\\ \Rightarrow -4(0)+5(0)<-3\\ \Rightarrow 0<-3\end{array}$

Since, the statement is false, the region that does not contain $(0,0)$ is shaded.

The shaded region is the graph of the inequality $-4x+5y<-3$ .